How to make texturure scrolling animation in Game Engine?
Well I've done something simple similar to what I've seen in your animation, using a mesh for each texture and using logic bricks with motion actuator to rotate the mesh, but you can animate the mesh if you prefer. I hope it is what you are looking for.

Note: 
It seems that the minimum value for the motion actuator is > 0.004 to appreciate the movement.

Press P to see it.